Research On Source Signal Recovery Of Undetermined Blind Source Separation Based On Compressed Sensing

Underdetermined blind source separation(UBSS) aims to recover source signals according to sensor signals without knowing channel transmission parameters. Compressed sensing is a compressed sampling technology developed in recent years. It can achieve signal sampling frequency lower than Nyquist sampling rate and completely recover the source signal from the received signal. Because the source signal recovery in UBSS has the same mathematical model with sparse signal reconstruction in compressed sensing, the sparse signal reconstruction algorithms are widely used to solve the source recovery in UBSS. This thesis mainly researches on source signal recovery in UBSS based on compressed sensing. The work of this thesis can be summarized as following aspects:Point out that the complete recovery conditions of UBSS proposed by Pando Georgiev is not completely correct. By comparing the complete recovery conditions of UBSS with the NSP property in compressed sensing, inconsistency of the conclusion is found. The problem of the UBSS separation conditions is found out and the conclusion is improved.The subspace complementary matching pursuit is proposed to reduce complexity of complementary matching pursuit. Greedy algorithms have good performance when source signal is sufficiently sparse. Some existing algorithms such as orthogonal matching pursuit algorithm have low complexity but not very high precision, and other more accurate algorithms such as complementary matching pursuit algorithm have high complexity. In order to reduce algorithm complexity without sacrifice of accuracy, subspace complementary matching pursuit is proposed based on combination between subspace pursuit and complementary matching pursuit. From theoretical analysis and experiments, it is founded that subspace complementary matching pursuit dramatically reduces the complexity without sacrifice of recovery precision.The L1 based complementary matching pursuit is proposed to reduce the complexity of existing L1 based algorithms. The existing L1 based algorithms have a good performance when source signal is sufficiently sparse. However, existing L1 based algorithms have the problem of high complexity. In order to solve the problem, L1 based complementary matching pursuit is proposed. The proposed algorithm reduces the dimension of optimization problem and the optimal is obtained by iterative convergence method. Through theoretical analysis and experiments, it is found that the proposed algorithm dramatically reduces the complexity without sacrifice of recovery precision.Modified Newton radial basis function is proposed to improve the convergence speed and recovery accuracy of smoothed L0 based algorithm. For traditional smoothed L0 based algorithm, the convergence speed is slow and the accuracy is influenced by step size. To solve these problems, the proposed algorithm combines the radial function with modified Newton function to improve the convergence speed and overcome the influence of step size. The experiments demonstrate that the proposed algorithm improves the convergence speed and recovery accuracy.